RTM using effective boundary saving: A staggered grid GPU implementation

Introduction

One-way equation based imaging techniques are inadequate to obtain accurate images in complex media due to propagation direction changes in the background model (Biondi, 2006). These approaches are extremely limited when handling the problems of turning waves in the model containing sharp wave-speed contrasts and steeply dipping reflectors. As an advanced imaging technology without dip and extreme lateral velocity limitation, reverse time migration (RTM) was proposed early (McMechan, 1983; Baysal et al., 1983), but not practical in terms of stringent computation and memory requirement. However, it gained increasingly attention in recent years due to the tremendous advances in computer capability. Until recently, 3D prestack RTM is now feasible to obtain high fidelity images (Guitton et al., 2006; Yoon et al., 2003).

Nowadays, graphics processing unit (GPU) is a booming technology, widely used to mitigate the computational drawbacks in seismic imaging and inversion, from one-way depth migration (Lin and Wang, 2012; Liu et al., 2012b) to two-way RTM (Hussain et al., 2011; Clapp et al., 2010; Micikevicius, 2009), from 2D to 3D (Foltinek et al., 2009; Abdelkhalek et al., 2009; Michéa and Komatitsch, 2010; Micikevicius, 2009; Liu et al., 2013a), from acoustic media to elastic media (Weiss and Shragge, 2013), from isotropic media to anisotropy (Liu et al., 2009; Suh and Wang, 2011; Guo et al., 2013). The investigators have studied many approaches: the Fourier integral method (Liu et al., 2012c), spectral element method (Komatitsch et al., 2010b), finite element method (Komatitsch et al., 2010a) as well as the rapid expansion method (REM) with pseudo-spectral approach (Kim et al., 2013). A variety of applications were conducted, for instance, GPU-based RTM denoising (Ying et al., 2013), iterative velocity model building (Ji et al., 2012), multi-source RTM (Boonyasiriwat et al., 2010), as well as least-square RTM (Leader and Clapp, 2012).

The superior speedup performance of GPU-based imaging and inversion has been demonstrated by numerous studies. One key problem of GPU-based RTM is that the computation is much faster while the data exchange between host and device always takes longer time. Many researchers choose to reconstruct the source wavefield instead of storing the modeling time history on the disk, just saving the boundaries. Unlike most GPU-based imaging and inversion studies, this paper is devoted to the practical technical issues instead of speedup performance. Starting from the computational strategies by Dussaud et al. (2008), we determine the minimum storage requirement in backward wavefield reconstruction for regular and staggered grid finite difference. We implement RTM with staggered finite difference scheme combined with convolutional perfectly matched layer (CPML) boundary condition using GPU programming. We demonstrate the validity of the proposed approach and CUDA codes with numerical test and imaging of benchmark models.

RTM using effective boundary saving: A staggered grid GPU implementation